45foot ladder is leaning against a building. The base of the ladder is 27 feet from the side of the building. How high does the ladder reach along the side of the building?

ladder reaches ___ feet high on the building.

Time for Pythagoras!

a^2 + b^2 = c^2

27^2 + b^2 = 45^2

729 + b^2 = 2025

b^2 - 1296

b = 36

To figure out how high the ladder reaches along the side of the building, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, the length of the ladder) is equal to the sum of the squares of the other two sides.

Let's denote the height the ladder reaches as "h".
We can then set up the following equation:

h^2 + 27^2 = 45^2

Simplifying the equation:

h^2 + 729 = 2025

Subtracting 729 from both sides:

h^2 = 2025 - 729
h^2 = 1296

Taking the square root of both sides:

h = √1296
h = 36

Therefore, the ladder reaches 36 feet high on the building.

To find out how high the ladder reaches along the side of the building, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

In this case, the ladder is the hypotenuse, the base distance is one side (a), and the height we want to find is the other side (b).

We have the following information:

Length of the base (a) = 27 feet
Length of the ladder (c) = 45 feet

Using the Pythagorean theorem, we can set up the equation:

c^2 = a^2 + b^2

Substituting the given values, we get:

45^2 = 27^2 + b^2

2025 = 729 + b^2

Subtracting 729 from both sides, we have:

2025 - 729 = b^2

1296 = b^2

To find b, we need to take the square root of both sides:

√1296 = √b^2

36 = b

Therefore, the ladder reaches 36 feet high along the side of the building.